UNDERSTANDING RADAR CROSS SECTION OF COMBAT AIRCRAFT AS A TARGET
Since you have reached this site, I will assume you are acquainted with the how, why and wherefores of radar, its operating principles and terminology, how it is utilised and how much it has evolved over the past seventyodd years. Quite naturally, the means and methods to defeat the effective implementation of radars have also evolved alongside.
According to GlobalSecurity.org, a nonpartisan, independent, nonprofit organisation that serves as a think tank, research and consultancy group, the radar cross section (RCS) of a target is defined as the effective area intercepting an amount of incident power which, when scattered isotropically, produces a level of reflected power at the radar equal to that from the target. RCS calculations require broad and extensive technical knowledge, thus many scientists and scholars find the subject challenging and intellectually motivating. This is a very complex field that defies simple explanation, and any short treatment is only a very rough approximation.
Another way to define RCS could be:
Radar cross section of a target is a measure of a targeted aircraft/aerial vehicle’s reflection of radar signals in the direction of the radar receiver, i.e. it is a measure of the ratio of backscatter power per steradian (unit solid angle) in the direction of the radar (from the target) to the power density that hits the target. The RCS of a target can be viewed as a comparison of the strength of the reflected signal from a target to the reflected signal from a perfectly smooth sphere of cross sectional area of 1 m2.
Concept of Radar Cross Section  The conceptual definition of RCS includes the fact that not all of the radiated energy falls on the target. A target's RCS (σ), which represents power reradiated from the target is most easily visualised as the product of three factors:
 σ = Projected cross section x Reflectivity x Directivity.
 Reflectivity: The percent of intercepted power reradiated (scattered) by the target.
 Directivity: The ratio of the power scattered back in the radar's direction to the power that would have been backscattered had the scattering been uniform in all directions (i.e. isotropically).
The units of radar cross section are square metres;
however, the radar cross section is NOT the same as the area of the target.
Because of the wide range of amplitudes typically encountered on a target, RCS
is frequently expressed in dBsm, or decibels relative to one square metre. The
RCS is the projected area of a metal sphere that is large compared with the
wavelength and that, if substituted for the object, would scatter identically
the same power back to the radar. However, the RCS of all but the simplest
scatterers fluctuates greatly with the orientation of the object, so the notion
of an equivalent sphere is not very useful.
Aircraft 
RCS (m2) 
RCS (dB) 
B52 
100 

F15 
25 

SU30 
15 

MiG21 
3 

F16 
5 

Mirage
2000 
5 

Bird 
0.01 

F16C 
1.2 

F18 
1.0 

Rafale 
1.0 

Eurofighter
Typhoon 
0.5 

Insect 
0.001 
30 
F35 
0.005 
30 
Different structures will exhibit different RCS
dependence on frequency than a sphere. However, three frequency regimes are
identifiable for most structures. In the Rayleigh region at low frequencies,
target dimensions are much less than the radar wavelength. In this region RCS
is proportional with the fourth power of the frequency. In the Resonance or Mie
Region at medium frequencies, target dimensions and the radar wavelength are in
the same order. The RCS oscillates in the resonance region. In the Optical
Region of high frequencies, target dimensions are very large compared to the
radar wavelength. In this region RCS is roughly the same size as the real area
of target. The RCS behaves more simply in the highfrequency region. In this
region, the RCS of a sphere is constant.
In general, codes based on the methodsofmoments (MOM)
solution to the electrical field integral equation (EFIE) are used to calculate
scattering in the Rayleigh and resonance regions. Codes based on physical
optics (PO) and the physical theory of diffraction (PTD) are used in the
optical or highfrequency region. The target's electrical size (which is proportional
to frequency and inversely proportional to the radar wavelength) that
determines the appropriate algorithm to calculate the scattering. When the
target length is less than 5 to 10 wavelengths, the EFIEMOM algorithm is used.
Alternatively, if the target wavelength is above 5 to 10 wavelengths, the
POPTD algorithm is used.
The RCS of a stealth aircraft is typically multiple
orders of magnitude lower than a conventional plane and is often comparable to
that of a small bird or large insect. "From the front, the F/A22's
signature is 40dBm2 (the size of a marble) while the F35's is 30 dBm2 (the
size of a golf ball). The F35 is said to have a small area of vulnerability
from the rear because engineers reduced cost by not designing a radar blocker
for the engine exhaust." The F35 stealthiness is a bit better than the
B2 bomber, which, in turn, was twice as good as that on the even older F117.
B2 stealth bomber has a very small cross section. The RCS of a B26 bomber
exceeds 35 dBm2 (3100m2 ) from certain angles. In contrast, the RCS of the B2
stealth bomber is widely reported to be about 40dBm2 .
A conventional fighter aircraft such as an F4 has an
RCS of about six square meters (m2), and the much larger but lowobservable B2
bomber, which incorporates advanced stealth technologies into its design, by
some accounts has an RCS of approximately 0.75 m2 [this is four orders of magnitude
greater than the widely reported 40dBm2 ]. Some reports give the B2 a headon
radar cross section no larger than a bird, 0.01 m2 or 20dBm2. A typical cruise
missile with UAVlike characteristics has an RCS in the range of 1 m2; the
Tomahawk ALCM, designed in the 1970s and utilising the fairly simple
lowobservable technologies then available, has an RCS of less than 0.05 m2.
The impact of lowered observability can be dramatic
because it reduces the maximum detection range from missile defenses, resulting
in minimal time for intercept. The US airborne warning and control system
(AWACS) radar system was designed to detect aircraft with an RCS of 7 m2 at a
range of at least 370 km and typical nonstealthy cruise missiles at a range of
at least 227 km; stealthy cruise missiles, however, could approach air defenses
to within 108 km before being detected. If such missiles travelled at a speed of
805 km per hour (500 miles per hour), air defenses would have only eight
minutes to engage and destroy the stealthy missile and 17 minutes for the
nonstealthy missile. Furthermore, a lowobservable LACM can be difficult to
engage and destroy, even if detected. Cruise missiles with an RCS of 0.1 m2 or
smaller are difficult for surfacetoair missile (SAM) firecontrol radars to
track. Consequently, even if a SAM battery detects the missile, it may not
acquire a sufficient lock on the target to complete the intercept.
Radar scattering from any realistic target is a
function of the body's material properties as well as its geometry. Once the
specular reflections have been eliminated by radar absorbing materials, only
nonspecular or diffractive sources are left. Nonspecular scatterers are
edges, creeping waves, and travelling waves. They often dominate backscattering
patterns of realistic targets in the aspect ranges of most interest. The
travelling wave is a high frequency phenomenon. Surface traveling waves are
launched for horizontal polarization and grazing angles of incidence on targets
with longs mooth surfaces. There is little attenuation from the flat smooth
surface, so the wave builds up as it travels along the target. Upon reaching a
surface discontinuity, for example an edge, the travelling wave is scattered and
part of it propagates back toward the radar. The sum of the travelling waves
propagating from the far end of the target toward the near end is the dominant
source to the target radar cross section.
The radar cross section (RCS) of a target not only
depends on the physical shape and its composite materials, but also on its
subcomponents such as antennas and other sensors. These components on the
platforms may be designed to meet low RCS requirements as well as their sensor
system requirements. In some cases, the onboard sensors can be the predominant
factor in determining a platform's total RCS. A typical example is a reciprocal
high gain antenna on a low RCS platform. If the antenna beam is pointed toward
the radar and the radar frequency is in the antenna operating band, the antenna
scattering can be significant.
The traditional measure of an object's scattering
behavior is the RCS pattern which plots the scattered field magnitude as a
function of aspect angle for a particular frequency and polarization. Although
suitable to calculate the power received by a radar operating with those
particular parameters, the RCS pattern is an incomplete descriptor of the
object's scattering behavior. While the RCS pattern indicates the effect of the
scattering mechanism, it does not reveal the physical processes which cause the
observed effect. In contrast, imaging techniques, which exploit frequency and
angle diversity to spatially resolve the reflectivity distribution of complex
objects, allow the association of physical features with scattering mechanisms.
These processes, therefore, indicate the causal components of the overall
signature level observed in RCS patterns.
TARGET 
RCS
M^{2} 
C130
Hercules 
80 
F15
Eagle 
1025 
Mig29
Fulcrum 
35 
F16A 
5 
Bird 
0.01 
F18
C/D 
13 
M2000 
12 
F16
C (with reduced RCS) 
1.2 
Eurofighter
Typhoon 
0.1
Class 
F16
IN Super Viper 
0.1
Class 
Rafale 
0.1
Class 
Source: GlobalSecurity.org
FLUCTUATION LOSS
The fluctuation of the reflected signal is based on the
complicated diagram of the relative radar crosssection (RCS). At a forward
movement the RCS diagram of the airplane is turned in the reference to the
radar set. Caused by the temporal changes of the aim course, the amplitudes and
phase changes effect a strong fluctuation of the reception field strength at
the radar antenna.
The Swerling models were introduced in 1954 by the
American mathematician Peter Swerling and are used to describe the statistical
properties of the radar crosssection of objects with complex formed surface.
According to the Swerling models the RCS of a reflecting object based on the
chisquare probability density function with specific degrees of freedom. These
models are of particular importance in the theoretically radartechnology. There
are five different Swerling models, numbered with the Roman numerals I through
V:
Swerling I Target
This case describes a target whose magnitude of the
backscattered signal is relatively constant during the dwell time. It varies
according to a Chisquare probability density function with two degrees of
freedom (m = 1). The radar crosssection is constant from pulsetopulse, but
varies independently from scan to scan. The density of probability of the RCS
is given by the RayleighFunction:
Where σ average
is the arithmetic mean of all values of RCS of the reflecting object.
Swerling II Target
The Swerling II target is similar to Swerling I, using
the same equation, except the RCS values changes faster and varies from pulse
to pulse additionally.
The Swerling cases I and II applies to a target that is
made up of many independent scatterers of roughly equal areas like airplanes.
However, in Swerling case II there is no rotating surveillance antenna but a
focused onto a target tracking radar.
Swerling III Target
The Swerling III target is decribed like Swerling I but
with four degrees of freedom (m = 2). The scantoscan fluctuation follows a
density of probability:
Swerling IV Target
The Swerling case IV is similar to Swerling III but the
RCS varies from pulse to pulse rather than from scan to scan and follows the above
Equation.
Swerling V
The Swerling case V is a reference value with a
constant radar crosssection (also known as Swerling 0). It describes an idealised
target without any fluctuation.